Now, the proof of Theorem 16 in [1]} directly establishes the fact that under the conditions of the lemma, we may replace all occurrences of some \(w_i\)  with \(|w_i| > e\)  consistently with any other word \(u\)  and still have a solution to the word equation. We need to ensure that this replacement also respects the regular language membership constraints, and this is the novel part of this proof. In particular, while in part (1) a similar replacement was done while preserving the length of the replaced strings, here we need to change the length of the solution.
